Spiral patterns and biodiversity in lattice-free Lotka-Volterra models

@article{Avelino2017SpiralPA,
  title={Spiral patterns and biodiversity in lattice-free Lotka-Volterra models},
  author={Pedro Avelino and Dionisio Bazeia and L. Losano and J. Menezes and B. F. de Oliveira},
  journal={arXiv: Populations and Evolution},
  year={2017}
}
Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest neighbor interactions starting from random initial conditions. In this Letter we describe the results of novel lattice-free Lotka-Volterra stochastic simulations, showing that, contrary to previous claims, the emergence of spiral patterns does occur for sufficiently high values of the (conserved) total density of individuals. We also investigate the dynamics in our… 

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References

SHOWING 1-10 OF 32 REFERENCES

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES.

-As an alternative to their description as vibrational levels, the low excited states of even-even nuclei can be described as rotational states of a helion, dineutron, diproton, or other cluster

“A and B”:

Direct fabrication of large micropatterned single crystals. p1205 21 Feb 2003. (news): Academy plucks best biophysicists from a sea of mediocrity. p994 14 Feb 2003.

Phys

  • Rev. E 84, 021912
  • 2011

Phys

  • Rev. E 83, 051108
  • 2011

Nature 448

  • 1046
  • 2007

Phys

  • Rev. E 82, 051909
  • 2010

Phys

  • Rev. E 77, 041919
  • 2008

The European Physical Journal B 82

  • 97
  • 2011

EPL (Europhysics Letters) 102

  • 28012
  • 2013

Nature (London) 118

  • 558
  • 1926